In a communication system, transmitted RF frequency waveforms are received and demodulated. Modern wireless communication systems aim at achieving high spectral efficiency at lowest possible cost, in channels which are limited in band and power.
When system constraints and physical channel characteristics suggest the use of single carrier modulations, the most straightforward way to achieve high spectral efficiency is to use high order modulations, e.g., M-QAM (Quadrature Amplitude Modulation), with M large. Very often, the resulting scenario is one where the channel seen at the receiver is no longer dominated by the physical channel, e.g., frequency selective fading and/or additive white noise, but by hardware impairments introduced by the transmission equipment itself.
One of the most common sources of impairment when dealing with high order dense modulations at high carrier frequencies is the phase noise arising from non-idealities in system oscillators, in turn caused by constraints on the power and cost of oscillator components, which then show nonlinearities and noise effects.
A classical solution to the problem of non-ideal oscillators (i.e. phase noise) is to use a phase-synchronous detector where the phase noise is compensated for by some type of phase tracking system, e.g., a PLL based system. Acquisition is almost always based on pilot insertion, that has a detrimental effect on overall efficiency, while steady-state tracking can be either data-aided (DA), when pilots are used, or non data-aided, e.g. when decision on received symbols are used. As an alternative to the PLL phase tracking approach, a phase detector based on a Kalman filter can be envisaged.
The detector performance can be further improved if the phase detection is performed jointly together with iterative decoding of a modern FEC code (i.e. an LDPC code). The general idea then is to exploit the higher quality symbol estimates available after some iterations of the FEC decoder to derive a refined estimate of the phase. The refined phase estimate is used to re-compute the FEC input, and the process is iterated. A number of alternative approaches to iterative phase tracking have been proposed in the literature. One approach involves the feedback of more reliable symbol decisions, either hard or soft, to the phase detector. Another approach dispenses with the phase detector altogether and replaces it with a factor graph representation of the phase process, which is used to iteratively estimate the time evolving phase. In this last solution the complexity of the receiver is very high, since the phase detector and the FEC decoder both use iterative algorithms described on graphs.
When spectral efficiency needs to be pushed further, beyond that achievable by conventional SISO (Single-Input Single-Output) transmission systems, MIMO (Multiple-Input Multiple-Output) systems can be exploited. The underlying system comprises a transmitter and a receiver, both with a certain number of antennas.
In the case of microwave transmission, this multidimensional channel is a Line-of-Sight channel with comparably small number of transmit and receive antennas. In spite of the low complexity of the channel matrix, the problem of dealing with phase noise in MIMO systems is significantly more complex than in the SISO case. While in the SISO case the phase errors at the transmitter and receiver sides simply sum to each other, in the MIMO case the phase processes observed at the receiver contains also the weighted contributions of the elementary, atomic phase processes, of all the transmitters. These atomic processes can not be observed directly at the receiver, therefore known methods commonly adopted in SISO systems can not be used to estimate their contribution to the total phase noise at the receiver side.
Extensions of the PLL based approaches have been proposed, but these extensions involve the critical assumption of having identical oscillators for all transmit and receive antennas, respectively. This is evidently a simplified approach which does not lead to satisfactory results. Further extensions of the joint phase tracking schemes are possible as well, with a higher complexity, especially in the case of the factor-graph based approaches.
All in all, straightforward extensions of solutions designed for the SISO case have several shortcomings. The simple replication of the PLL scheme used in SISO case leads to unacceptable performance since the estimate of the phase noise sum processes is not good enough to ensure recovery of the signal at the receiver.
Not straightforward extensions of the SISO PLL scheme have been proposed, but their high complexity is such that their practical use has been discarded.
Extension of the type of advanced SISO joint solutions based on factor graphs is not straightforward, mainly due to the conceptual problems associated with the correlation of the phase processes in the MIMO case.